Merge pull request #76 from snood1205/add-maths-algos

Add absolute value, aliquot sum, ceil, and square root

DIRECTORY.md

@@ -24,6 +24,12 @@
   * [Euclidean Gcd](https://github.com/TheAlgorithms/Ruby/blob/master/discrete_mathematics/euclidean_gcd.rb)
   * [Lcm](https://github.com/TheAlgorithms/Ruby/blob/master/discrete_mathematics/lcm.rb)
 
+## Maths
+  * [Absolute Value](https://github.com/TheAlgorithms/Ruby/blob/master/maths/abs.rb)
+  * [Aliquot Sum](https://github.com/TheAlgorithms/Ruby/blob/master/maths/aliquot.rb)
+  * [Ceil](https://github.com/TheAlgorithms/Ruby/blob/master/maths/ceil.rb)
+  * [Square Root](https://github.com/TheAlgorithms/Ruby/blob/master/maths/square_root.rb)
+
 ## Other
   * [Fisher Yates](https://github.com/TheAlgorithms/Ruby/blob/master/other/fisher_yates.rb)
 

maths/abs.rb

@@ -0,0 +1,10 @@
+# frozen_string_literal: true
+
+# Calculates the absolute value of a number
+class Abs
+  def self.call(number)
+    return -number if number.negative?
+
+    number
+  end
+end

maths/abs_test.rb

@@ -0,0 +1,18 @@
+# frozen_string_literal: true
+
+require 'minitest/autorun'
+require_relative './abs'
+
+class AbsTest < Minitest::Test
+  def test_positive_number
+    assert_equal Abs.call(4), 4
+  end
+
+  def test_zero
+    assert_equal Abs.call(0), 0
+  end
+
+  def test_negative_number
+    assert_equal Abs.call(-9), 9
+  end
+end

maths/aliquot_sum.rb

@@ -0,0 +1,21 @@
+# frozen_string_literal: true
+
+require_relative './square_root'
+require_relative './ceil'
+
+# Calculates the aliquot sum of a number (the sum of all proper divisors of a number)
+class AliquotSum
+  class << self
+    def call(number)
+      divisors(number).sum
+    end
+
+    private
+
+    def divisors(number)
+      low_divisors = (1..Ceil.call(SquareRoot.call(number))).select { |num| (number % num).zero? }
+      high_divisors = low_divisors.map { |div| number / div }
+      (low_divisors + high_divisors).uniq - [number]
+    end
+  end
+end

maths/aliquot_sum_test.rb

@@ -0,0 +1,21 @@
+# frozen_string_literal: true
+
+require 'minitest/autorun'
+require_relative './aliquot_sum'
+
+class AliquotSumTest < Minitest::Test
+  def test_zero
+    assert_equal AliquotSum.call(0), 0
+  end
+
+  def test_one
+    assert_equal Abs.call(1), 1
+  end
+
+  def test_many
+    (2..100).each do |number|
+      expected_aliquot_sum = (1...number).select { |num| (number % num).zero? }.sum
+      assert_equal AliquotSum.call(number), expected_aliquot_sum
+    end
+  end
+end

maths/ceil.rb

@@ -0,0 +1,11 @@
+# frozen_string_literal: true
+
+class Ceil
+  class << self
+    def call(number)
+      return number if number.is_a?(Integer) || number == number.to_i
+
+      number.to_i + 1
+    end
+  end
+end

maths/ceil_test.rb

@@ -0,0 +1,18 @@
+# frozen_string_literal: true
+
+require 'minitest/autorun'
+require_relative './ceil'
+
+class CeilTest < Minitest::Test
+  def test_integer
+    assert_equal Ceil.call(4), 4
+  end
+
+  def test_float_at_integer
+    assert_equal Ceil.call(4.0), 4
+  end
+
+  def test_float_not_at_integer
+    assert_equal Ceil.call(4.01), 5
+  end
+end

maths/square_root.rb

@@ -0,0 +1,26 @@
+# frozen_string_literal: true
+
+# Calculates the square root of a number
+class SquareRoot
+  class << self
+    EPSILON = 1E-10
+
+    def call(number)
+      raise DomainError, 'Cannot find square root of negative number' if number.negative?
+      return 0 if number.zero?
+
+      find_root(number)
+    end
+
+    private
+
+    def find_root(x0, xn = x0)
+      xn1 = xn - ((xn * xn - x0) / (2.0 * xn))
+      return xn1 if (xn1 - xn).abs <= EPSILON
+
+      find_root(x0, xn1)
+    end
+  end
+end
+
+class DomainError < StandardError; end

maths/square_root_test.rb

@@ -0,0 +1,22 @@
+# frozen_string_literal: true
+
+require 'minitest/autorun'
+require_relative './square_root'
+
+class SquareRootTest < Minitest::Test
+  def test_negative_number
+    assert_raises DomainError do
+      SquareRoot.call(-1)
+    end
+  end
+
+  def test_zero
+    assert_equal 0, SquareRoot.call(0)
+  end
+
+  def test_all_numbers_below_1024
+    (1...1024).each do |num|
+      assert_in_delta SquareRoot.call(num), Math.sqrt(num), 1E-12
+    end
+  end
+end